Thread: equation-geometrical

1. Find the value for c for which y=x+c is a tangent to y=3-x-5x^2

don't understand what to do

You gotta find first the intersection of the line and the curve, so



Now, so that the line be tangent to the curve, the discriminant of the previous equation must be zero, so

Solvin' for yields the desired answer.

The system formed by the two equations must have an unique solution.
Plug y from the first equation in the second and you'll obtain a quadratic equation. Put the condition that , where (a,b,c are the coefficients of the quadratic equation).